Parameter Estimation for Multiscale Diffusions

Details Parameter Estimation for Multiscale Diffusions Parameter Estimation for Multiscale Diffusions

2006-03-28

arxiv.org/abs/math/0603668v1

Mathematics

Statistics Theory

35 pages, 14 figures, submitted to JRSSB

Scientific paper

10.1007/s10955-007-9300-6

We study the problem of parameter estimation for time-series possessing two, widely separated, characteristic time scales. The aim is to understand situations where it is desirable to fit a homogenized singlescale model to such multiscale data. We demonstrate, numerically and analytically, that if the data is sampled too finely then the parameter fit will fail, in that the correct parameters in the homogenized model are not identified. We also show, numerically and analytically, that if the data is subsampled at an appropriate rate then it is possible to estimate the coefficients of the homogenized model correctly.

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